Big-O Interview Challenges: Real-World Problem Scenarios Quiz Quiz

Assess your understanding of Big-O notation in practical situations with this quiz focused on real-world algorithm challenges and their efficiency. Sharpen your skills in identifying time and space complexities through applied examples and problem-solving scenarios relevant to coding interviews.

1. Analyzing Sorted List Search

   Given a sorted list of 1 million unique integers, what is the Big-O time complexity of finding a specific number using the standard binary search algorithm?

   1. O(1)
   2. O(log n)
   3. O(n log n)
   4. O(n)

   Explanation: Binary search reduces the search space by half with each step, resulting in O(log n) time complexity. O(n) would be the case for linear search, which is not applicable to binary search in a sorted list. O(1) suggests constant time, which is not possible for searching in a list using this approach. O(n log n) is usually associated with efficient sorting algorithms, not searching.

2. Efficiency of Duplicate Checking

   If you have an unsorted array and want to check if it contains any duplicates, what is the time complexity using a hash set to track seen numbers as you iterate through the array?

   1. O(n^2)
   2. O(n)
   3. O(1)
   4. O(log n)

   Explanation: Using a hash set to store seen elements allows you to check for duplicates in one pass, leading to O(n) time complexity. O(n^2) would occur if you used a nested loop to compare each pair, which is unnecessary here. O(log n) is not achievable since every item must be checked. O(1) implies constant time, which isn't possible for checking an entire array.

3. Nested Loop Matrix Traversal

   In a function that iterates through an n x n matrix using nested loops (one for rows, one for columns), what is the time complexity of visiting each element once?

   1. O(2n)
   2. O(n)
   3. O(n^2)
   4. O(log n)

   Explanation: Iterating through each row and then through each column for that row results in O(n^2) operations because you visit every cell. O(n) would mean only a single loop over either rows or columns, not both. O(2n) simplifies to O(n) and incorrectly suggests linearity. O(log n) would incorrectly imply a divide-and-conquer or binary search approach, not applicable here.

4. Impact of Removing Duplicates

   Suppose you are given an unsorted array and need to remove all duplicates while preserving the first occurrence order. If you use a hash set to check and a new array to store results, what is the overall time complexity?

   1. O(n)
   2. O(n^2)
   3. O(1)
   4. O(n log n)

   Explanation: With a hash set, each check for duplicates and insertion takes O(1) on average, so iterating through the array once leads to O(n). O(n^2) would be the case for a naïve solution with nested loops. O(1) isn't feasible because each element must be processed. O(n log n) usually refers to comparison-based sorting, which is not required here.

5. Space Complexity of Recursive Solutions

   What is the Big-O space complexity for a recursive function that computes the n-th Fibonacci number using pure recursion without memoization?

   1. O(1)
   2. O(log n)
   3. O(n^2)
   4. O(n)

   Explanation: A pure recursive Fibonacci calculation generates a call stack up to n levels deep, resulting in O(n) space complexity. O(1) would only be valid for an iterative or optimized approach without stack overhead. O(n^2) is incorrect as the stack does not grow quadratically. O(log n) applies to divide-and-conquer algorithms like binary search, not to this recursion.